Describe how the two figures at the right are alike and how they are different which box has a larger lateral surface area?
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=> Surface area:
The surface area of a solid is the sum of the areas of the plane or curved faces of the solid.
It is measured in square units such as square centimetre (cm²) and square metre (m²).
Surface area of cube is the sum of the surface areas of its six rectangular faces.
Surface Area of Cube is = 6a²
By surface area of a cube we mean the total surface area.
The sum of the areas of 4 vertical faces of a cube is called its lateral surface area.
The lateral surface area of the cube= 4a²
Cylinder:
Whenever we talk about a total surface area of a cylinder the cylinder must be closed at both the ends by two circular regions or it should be a cylindrical solid object.
Total surface area of a solid cylinder= curved surface area + sum of the areas of two circular ends of the cylinder
= 2πrh+ 2πr²
Total surface area of a solid cylinder= 2πr(h+r)
The lateral surface area of the curved surface area of a cylinder= 2πrh
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Solution:
Both the figure have same height & one figure is cube & the other one is cylinder.
Given: Diameter of cylinder = 7 cm
Radius of cylinder (r)= 7/2 cm
Height of cylinder(h) = 7 cm
Side of CUBE(a)= 7 cm
Lateral surface area of cylinder = 2πrh
= 2(22/7)(7/2)(7)
= 22× 7
= 154 cm²
Lateral surface area of cylinder = 154 cm²
Lateral surface area of cube= 4 a²
= 4 ×(7)²
= 4× 49
= 196 cm²
Lateral surface area of cube= 196 cm²
Hence, the cube has larger lateral surface area.
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Step-by-step explanation:
Similarity Both the figures have same length (= 7 cm) and same height (= 7 cm) Difference Figure (a) has circular bottom and top & Figure (b) has square bottom and top. Figure (a) is a cylinder and Figure (b) is a cube. Figure (a) is a cylinder and Figure (b) is a cube. We also need to find which box has larger surface area Lateral Surface Area of Cylinder Radius = r = 7/2 cm Height = h = 7 cm Lateral surface area of cylinder = 2ℎ = 2×22/7×7/2×7 = 22 × 7 = 154 cm2 Lateral Surface Area of Cube Side of cube = 7 cm Lateral surface area of cube = 4(Side)2 = 4 × 72 = 4 × 49 = 196 cm2 So, Cube has larger lateral surface area
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